Originally posted by Pockets
Just for a quick thought experiment, Trackwalker...
m*g*h=1/2*m*v^2
I have to guess on "m", but the internet says that a single car weighs between 400 and 600 kg, so let's say 4000 kg for an average train.
so
4000 kg *9.81 m/s^2* 274.32 m = 1/2*4000 kg* v^2
and
v=73.36 m/s, or about 164 mph. (is it just me, or does that seem low)
But that's without air friction.
For that, I need to make more assumptions. Says the internet, a rollercoaster train has the approximate dimensions of 1.2 m x 1.1 m. So A= 1.32 m^2. Also the drag coefficient for a long, streamline body is .1, so assuming slightly less than optimally smooth, let's say Cd= .15. Finally, the density of air is normally around 1.2 kg/m^3.
Now, I don't feel like doing differential equations, but the research is done, for anyone who wants to continue.
You do not need the mass value, silly.
The mass is in both the potential and kinetic energy so it can be removed from the equation.
It's strange that you know those formulas, but have forgotten free fall speed does not depend on mass.